-LRB- CNN -RRB- -- Fernando Torres rediscovered his scoring touch as Liverpool continued their revival under new owners with a 2-0 win over English Premier League leaders Chelsea at Anfield on Sunday .

The Spanish star scored two magnificent first half goals to seal three points for Roy Hodgson 's men .

The first came after 11 minutes as he instantly controlled a Dirk Kuyt through ball before beating Petr Cech with a low shot .

He doubled the advantage just before the interval as he cut inside before curling home a superb shot .

Chelsea manager Carlo Ancelotti introduced striker Didier Drogba , who had an overnight illness , after the break and it sparked an improvement by his side after a lifeless first half .

Home keeper Pepe Reina blocked a close range shot from Florent Malouda after a cross by Droga .

Cech prevented his team from going three down when he stretched out a leg to deny Dirk Kuyt before Chelsea nearly cut the deficit only for Nicolas Anelka 's strike to hit the crossbar .

Jamie Carragher summed up the spirit in the Liverpool side as he made a last-ditch tackle to deny Drogba scoring from the rebound .

The defeat leaves Chelsea just two points clear of Manchester United , who beat Wolves 2-1 on Saturday .

Hodgson , who was under pressure before his side 's improvement since New England Sports Ventures took control of the club , was delighted to see Torres back to his best .

`` He is a vital player for us and would be any club . You ca n't have success if you do n't have front players who do a good job for you , '' he told Sky Sports .

Third-placed Arsenal were also beaten in Sunday 's early game as they slid to a 1-0 home defeat to promoted Newcastle at the Emirates .

Arsenal were hoping to regain second spot in the standings ahead of Manchester United , but a goal from in-form striker Andy Carroll just before halftime sealed victory for Chris Hughton 's men .

Carroll , who was watched by England manager Fabio Capello , rose high to head home a well-flighted free kick from Joey Barton past Lucasz Fabianski .

It was the third straight win for improving Newcastle , who were rarely troubled by a labored Arsenal side .

Cesc Fabregas rattled the crossbar with a first half free kick and Theo Walcott hit the woodwork after the break , but a miserable afternoon for the Gunners was complete when Laurent Koscielny was sent off in added time .

He pulled back Nile Ranger as Newcastle broke upfield in a quick counter attack .

In Sunday 's other fixture , Manchester City ended a run of three straight defeats with a 2-0 win at West Bromwich Albion .

Italian striker Mario Balotelli scored both City 's goals in the first half , but blotted his copybook by being sent off after the break .

He was shown red for kicking out at Youssuf Mulumbu minutes after being booked .

Mulumbu was then sent off for a strong challenge on the returning Carlos Tevez , who had a hand in both goals .

The win takes Roberto Mancini 's men level on points with Arsenal as they stay in the Champions League places after 11 rounds .

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Brilliant Fernando Torres double inspires Liverpool win over Chelsea

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Andy Carroll scores only goal of the match as Newcastle shock Arsenal 1-0

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Mario Balotelli grabs first half brace as Manchester City win 2-0 at WBA